Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage ofthe total variation that can be explained by the linear relationship between the two variables. r = 0.885 (x = weight of male, y = waist size of male)

Answer:

Step-by-step explanation:

We would apply the formula for exponential growth which is expressed as

y = b(1 + r)^t

Where

y represents the population, t years after 2010.

t represents the number of years.

b represents the initial population.

r represents rate of growth.

From the information given,

b = 2.13 × 10^6

r = 2.4% = 2.4/100 = 0.024

Therefore, the equation that you can use to predict the population for the number of years after 2010 is

y = 2.13 × 10^6(1 + 0.024)^t

y = 2.13 × 10^6(1.024)^t

Answer: the length of the kite string is 183.6 feet

Step-by-step explanation:

The string of the kite forms an angle of 57° with the ground thus, a right angle triangle is formed. Richard's distance from the point on the ground directly below the kite represents the adjacent side of the right angle triangle. The length of the kite, h represents the hypotenuse of the right angle triangle. To determine h, we would apply the cosine trigonometric ratio.

Cos θ = adjacent side/hypotenuse. Therefore,

Cos 57 = 100/h

h = 100/Cos57

h = 100 /0.5446

h = 183.6 feet

Answer:

  a. 90°

  b. 180°

  c. 180°

Step-by-step explanation:

For these problems there is a bit of a shortcut you can take. Each figure is entirely within one quadrant, and the rotation is said to be by 90° (one quadrant), 180° (two quadrants), or 270° (three quadrants) clockwise.

a. The image is in the adjacent clockwise quadrant, so rotation is 90°.

b, c. The image is in the diagonally opposite quadrant, so rotation is 180°.

Answer:

it was B

Step-by-step explanation:

The algorithm employing "Nearest Neighbour" to determine one of the cheaper routes to visit every city and get back home again would be:

B). ATL-CHI-BOS-DEN-ATL

Thus, option B is the correct answer.

Learn more about "Algorithm" here

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The probability of rolling a sum of 5 when rolling two fair, six-sided dice is 1/18.

The probability that the sum of the two rolls is 5 can be found by considering the possible outcomes. There are a total of 36 equally likely outcomes when rolling two fair, six-sided dice.

Out of these, the prime sums are 5, 7, 11, and 17. The sum of 5 can only be obtained by rolling a 1 and a 4 or a 2 and
a 3. Since each die has 6 sides, the probability of rolling a 1 and a 4 is 1/6 × 1/6 = 1/36.

Similarly, the probability of rolling a 2 and a 3 is also 1/36. Therefore, the overall probability of rolling a sum of 5 is
1/36 + 1/36 = 2/36 = 1/18.

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Answer:

Supply curve vs Aggregate Supply

Step-by-step explanation:

- Supply express a direct relationship between what producers supply and how that relationship affects the price of a specific product or service. Hence, expresses a linear increase - or a constant slope

- Aggregate supply are the total supply in an economy at a particular period of time and a particular price threshold. Aggregate supply is an economy's gross domestic product (GDP), the total amount a nation produces and sells.

-  Aggregate supply convey how much firms are willing to produce at a specific price point.

- Aggregate supply is a response to increasing prices that drive firms to utilize more inputs to produce more output. The incentive is that if the price of inputs remains the same but if the price of outputs increase, the firm will generate larger profits and margins by producing and selling more. The aggregate supply curve is represented by a curve that slopes upward, which indicates that as the price per unit goes up, a firm will supply more. Increasing slope - Not constant.

- The supply curve eventually becomes vertical, indicating that at a certain price point a firm cannot produce anymore, as they are limited by certain inputs, e.g. number of employees and number of factories.

Answer:

28 minutes spent in washing the dishes.

Step-by-step explanation:

Given the table

Chore             time in minutes

Sweeping           42

Dishes                  ?

Amanda spent a total of 70 minutes competing her chores this week

Total of 70 minutes spent

42 minutes spent in sweeping . to find the number of minutes Amanda spent in washing the dishes , subtract 42 minutes from the total time spent

let x be the number of minutes spent washing the dishes

[tex]42+x=70[/tex]

To solve for x , subtract 42 from both sides

[tex]42+x=70\\x= 70-42\\x=28[/tex]

28 minutes spent in washing the dishes.

Answer:

D

Step-by-step explanation:

Depending on the number of defects in 6th car,  we have 3 cases:

To find mean we can use the sum of numbers given (= 36) and add either 3, 7, or 12 to it and then divide by 6 (number of cars).

(36 + 3) /6 = 39/6 = 6.5 (== median above)

(36 + 7) /6 = 43/6 = 7.1 (does not equal median above)

(36 + 12) /6 = 48/6 = 8 (== median above)

Answer: D (I and III only).

Answer:

$118,791.2985

Step-by-step explanation:

Given that,

A = 160,000

T = 18 - 8 = 10 years

Rate = 3%

since it is semi annual, n = 2

A = P ( 1 + R/2) ∧ 2T

160000 = P ( 1 + 3/2*100) ∧ 2 * 10

160000 = P ( 1 + 3/200) ∧20

160000 = P( 1 + 0.015) ∧20

160000 = P(1.015)∧20

P= 160000/ (1.015)∧20

P = 160000/ 1.3469

= $118,791.2985

Answer:

Total length of the Nylon rope will be 5.8 feet.

Step-by-step explanation:

Given:

Height of the tent = 5 ft

ground Distance from stake to tent = 3 ft

We need to find the Total length of the nylon rope.

Solution:

Now we can say that the total length of the nylon rope, the height of the tent, the ground distance from the stake to the tent, forms a right angle triangle.

From above we can see that;

the height of the tent, the ground distance from the stake to the tent are the two legs of the right angled triangle.

While the Total length of the nylon rope is the hypotenuse.

Now using Pythagoras theorem we get;

[tex]h^2=l_1^2+l_2^2[/tex]

[tex]l_1[/tex] ⇒ the height of the tent

[tex]l_2[/tex] ⇒  the ground distance from the stake to the tent

[tex]h[/tex] ⇒ the Total length of the nylon rope

substituting the values we get;

[tex]h^2=5^2+3^2\\\\h^2=25+9\\\\h^2=34[/tex]

Taking square root on both side we get;

[tex]\sqrt{h^2} =\sqrt{34} \\\\h=5.8\ ft[/tex]

Hence Total length of the Nylon rope will be 5.8 feet.

Answer:

Just find the hypotenuse by doing a^2 + B^2 = C^2

Step-by-step explanation:

Step-by-step explanation:

[tex](f - g)(x) = f(x) - g(x) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (2x - 4) - ( {x}^{2} + 3) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2x - 4 - {x}^{2} - 3 \\ \red{ \boxed{\therefore (f - g)(x) = - {x}^{2} + 2x - 7}}[/tex]

Answer:

(1) The expected number of people who would have consumed alcoholic beverages is 34.9.

(2) The standard deviation of people who would have consumed alcoholic beverages is 10.56.

(3) It is surprising that there were 45 or more people who have consumed alcoholic beverages.

Step-by-step explanation:

Let X = number of adults between 18 to 20 years consumed alcoholic beverages in 2008.

The probability of the random variable X is, p = 0.697.

A random sample of n = 50 adults in the age group 18 - 20 years is selected.

An adult, in the age group 18 - 20 years, consuming alcohol is independent of the others.

The random variable X follows a Binomial distribution with parameters n = 50 and p = 0.697.

The probability mass function of a Binomial random variable X is:

[tex]P(X=x)={50\choose x}0.697^{x}(1-0.697)^{50-x};\ x=0,1,2,3...[/tex]

(1)

Compute the expected value of X as follows:

[tex]E(X)=np\\=50\times 0.697\\=34.85\\\approx34.9[/tex]

Thus, the expected number of people who would have consumed alcoholic beverages is 34.9.

(2)

Compute the standard deviation of X as follows:

[tex]SD(X)=\sqrt{np(1-p)}=\sqrt{50\times 0.697\times (1-0.697)}=10.55955\approx10.56[/tex]

Thus, the standard deviation of people who would have consumed alcoholic beverages is 10.56.

(3)

Compute the probability of X ≥ 45 as follows:

P (X ≥ 45) = P (X = 45) + P (X = 46) + ... + P (X = 50)

                [tex]=\sum\limits^{50}_{x=45} {50\choose x}0.697^{x}(1-0.697)^{50-x}\\=0.0005+0.0001+0.00002+0.000003+0+0\\=0.000623\\\approx0.0006[/tex]

The probability that 45 or more have consumed alcoholic beverages is 0.0006.

An unusual or surprising event is an event that has a very low probability of success, i.e. p < 0.05.

The probability of 45 or more have consumed alcoholic beverages is 0.0006. This probability value is very small.

Thus, it is surprising that there were 45 or more people who have consumed alcoholic beverages.

Final answer:

The set of ordered pairs that correctly satisfies the equation y = 1/8x + 11 is (0,11) (8,12) (16,13). This is determined by substituting the x-values into the equation to check if the y-values correspond.

Explanation:

The question is asking which set of ordered pairs satisfies the equation y = 1/8x + 11. To determine the correct set, we will plug in the x-values from each ordered pair into the equation and see if the resulting y-value matches the one provided in the ordered pair. Let's examine each set:

(0,11) - If we plug in x=0, we get y=1/8*0+11=11. This matches the ordered pair, so (0,11) is correct.

(5,12) - With x=5, y becomes 1/8*5+11=11.625. This does not match the ordered pair (5,12), so this set is incorrect.

(7,13) - With x=7, y is 1/8*7+11=11.875. This does not match the ordered pair (7,13), so this set is also incorrect.

(8,12) - With x=8, y is 1/8*8+11=12. This matches the ordered pair, so (8,12) is correct.

(16,13) - With x=16, y is 1/8*16+11=13. This matches the ordered pair, so (16,13) is correct.

(6,12) - With x=6, y is 1/8*6+11=11.75. This does not match the ordered pair (6,12), so this set is incorrect.

(8,13) - Again, with x=8, y should be 12, not 13, so the ordered pair (8,13) is incorrect.

The only set with all matching ordered pairs for the equation y = 1/8x + 11 is (0,11) (8,12) (16,13).

Answer:

3x-7y=-6

Step-by-step explanation:

Answer:

[tex]A(x)=x(\sqrt{2500-x^{2} } )[/tex] is the area expressed as function of x,

and x: >0, <50 is the domain of the function.

Step-by-step explanation:

Draw an appropriate figure and then express the area of the rectangle as a function of x.

We know that the diagonal of a rectangle inscribed in a circle, will be equal to the diameter of the circle. 50 feet

let w = the width of the rectangle

therefore

[tex]x^2 + w^2 = 50^2\\w^2 = 2500 - x^2\\w = \sqrt{2500-x^{2} }[/tex]

recall

Area = x*w

replace w

[tex]A(x)=x(\sqrt{2500-x^{2} } )[/tex] is the area expressed as function of x

b)state the domain of the function

x: >0, <50

To find the area of the rectangle inscribed in a circle, we can use the Pythagorean theorem to find the length of the rectangle. Then, we can calculate the area by multiplying the width and length. The function that represents the area of the rectangle as a function of x is A(x) = x * sqrt(2500 - x^2), and the domain is x >= 0 and x <= 50.

To find the area of the rectangle, we need to consider that the diagonal of the rectangle is equal to the diameter of the circle, which is twice the radius. Therefore, the diagonal measures 50 feet.

We can use the Pythagorean theorem to find the length of the rectangle. Let's denote the length as y. We have:

x^2 + y^2 = 50^2

This equation represents the relationship between the width and length of the rectangle. By solving for y, we can express the length as a function of x.

Once we have the width and length of the rectangle, we can calculate the area by multiplying them:

A = x * y = x * sqrt(50^2 - x^2)

The function that represents the area of the rectangle as a function of x is A(x) = x * sqrt(2500 - x^2). The domain of this function is x >= 0 and x <= 50.

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Answer:

(a) P(X = 0) = 1/3

(b) P(X = 1) = 2/9

(c) P(X = −2) = 1/9

(d) P(X = 3) = 0

(a) P(Y = 0) = 0

(b) P(Y = 1) = 1/3

(c) P(Y = 2) = 1/3

Step-by-step explanation:

Given:

- Two 3-sided fair die.

- Random Variable X_1 : Result on 1st die.

- Random Variable X_2: Result on 2nd die.

- Random Variable X = X_2 - X_1.

Solution:

- Possible outcomes of X : { - 2 , -1 , 0 ,1 , 2 }

- The corresponding probabilities for each outcome are:

                 ( X = -2 ):  { X_2 = 1 , X_1 = 3 }  

                P ( X = -2 ):  P ( X_2 = 1 ) * P ( X_1 = 3 )  

                                :  ( 1 / 3 ) * ( 1 / 3 )  

                                : ( 1 / 9 )    

                ( X = -1 ):  { X_2 = 1 , X_1 = 2 } + { X_2 = 2 , X_1 = 3 }

                P ( X = -1 ):  P ( X_2 = 1 ) * P ( X_1 = 3 ) + P ( X_2 = 2 ) * P ( X_1 = 3)

                                :  ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 )

                                : ( 2 / 9 )        

 ( X = 0 ):  { X_2 = 1 , X_1 = 1 } + { X_2 = 2 , X_1 = 2 } +  { X_2 = 3 , X_1 = 3 }

               P ( X = -1 ):3*P ( X_2 = 1 )*P ( X_1 = 1 )

                                :  3*( 1 / 3 ) * ( 1 / 3 )

                                : ( 3 / 9 ) = ( 1 / 3 )        

                  ( X = 1 ):  { X_2 = 2 , X_1 = 1 } + { X_2 = 3 , X_1 = 2 }

               P ( X = 1 ): 2* P ( X_2 = 2 ) * P ( X_1 = 1 )

                                : 2* ( 1 / 3 ) * ( 1 / 3 )

                                : ( 2 / 9 )

                  ( X = 2 ):  { X_2 = 1 , X_1 = 3 }

                 P ( X = 2 ):  P ( X_2 = 3 ) * P ( X_1 = 1 )  

                                   :  ( 1 / 3 ) * ( 1 / 3 )  

                                   : ( 1 / 9 )                  

- The distribution Y = X_2,

                         P(Y=0) = 0

                         P(Y=1) =  1/3

                         P(Y=2) = 1/ 3

- The probability for each number of 3 sided die is same = 1 / 3.

In this exercise we have to use the knowledge of probability to calculate the chance of an event to occur, so:

A) P(X = 0) = 1/3

B) P(X = 1) = 2/9

C) P(X = −2) = 1/9

D) P(X = 3) = 0

A) P(Y = 0) = 0

B) P(Y = 1) = 1/3

C) P(Y = 2) = 1/3

organizing the following information given in the text we have that:

Then calculating the probability we find that:

A)  For P(X = 0) we have

[tex]( X = -2 ): { X_2 = 1 , X_1 = 3 } \\P ( X = -2 ): P ( X_2 = 1 ) * P ( X_1 = 3 ) \\ : ( 1 / 3 ) * ( 1 / 3 ) \\ : ( 1 / 9 )[/tex]

B)   For  P(X = 1) er have:

[tex]( X = -1 ): { X_2 = 1 , X_1 = 2 } + { X_2 = 2 , X_1 = 3 }\\ P ( X = -1 ): P ( X_2 = 1 ) * P ( X_1 = 3 ) + P ( X_2 = 2 ) * P ( X_1 = 3)\\ : ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 )\\ : ( 2 / 9 )[/tex]  

C) For  P(X = −2)  we have:

[tex]( X = 0 ): { X_2 = 1 , X_1 = 1 } + { X_2 = 2 , X_1 = 2 } + { X_2 = 3 , X_1 = 3 }\\ P ( X = -1 ):3*P ( X_2 = 1 )*P ( X_1 = 1 )\\ : 3*( 1 / 3 ) * ( 1 / 3 )\\ : ( 3 / 9 ) = ( 1 / 3 )[/tex]    

D) For P(X = 3), we have:

[tex]( X = 1 ): { X_2 = 2 , X_1 = 1 } + { X_2 = 3 , X_1 = 2 }\\ P ( X = 1 ): 2* P ( X_2 = 2 ) * P ( X_1 = 1 )\\ : 2* ( 1 / 3 ) * ( 1 / 3 )\\ : ( 2 / 9 )\\ ( X = 2 ): { X_2 = 1 , X_1 = 3 }\\ P ( X = 2 ): P ( X_2 = 3 ) * P ( X_1 = 1 ) \\ : ( 1 / 3 ) * ( 1 / 3 ) \\ : ( 1 / 9 )[/tex]            

In this next case we have to take into account that the number will be the probability of falling 3, that is:

A) P(Y=0) = 0

B) P(Y=1) =  1/3

C) P(Y=2) = 1/ 3

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Answer:

Given: ​ BD ​is an altitude of △ABC .

Prove: sinA/a=sinC/c

Triangle ABC with an altitude BD where D is on side AC. Side AC is also labeled as small b. Side AB is also labeled as small c. Side BC is also labeled as small a. Altitude BD is labeled as small h.

Statement Reason

​ BD is an altitude of △ABC .

Given △ABD ​ and ​ △CBD ​ are right triangles. (Definition of right triangle)

sinA=h/c and sinC=h/a

Cross multiplying, we have

csinA=h and asinC=h

(If a=b and a=c, then b=c)

csinA=asinC

csinA/ac=asinC/ac (Division Property of Equality)

sinA/a=sinC/c

This rule is known as the Sine Rule.

Answer:

For the people on Edge the answers are:

a/f

cf

c/b

cf + ec

c

To estimate the percentage of seniors attending college with a 4% margin of error and 90% confidence, a sample size of 424 is needed. For constructing a confidence interval and hypothesis testing about military enlistment, various statistical formulas are applied, including adjustments for undecided responses.

To estimate the percentage of this year’s seniors planning to attend college with a margin of error no greater than 4% and 90% confidence, we use the formula for determining sample size for a proportion, which is n = (Z^2 * p * (1-p)) / E^2, where Z is the Z-score corresponding to the confidence level, p is the estimated proportion, and E is the margin of error. With a 90% confidence level, the Z-score is approximately 1.645, and assuming we don't have a preliminary estimate, we use p = 0.5 for maximum variability, thus maximizing the required sample size.

To calculate: n = (1.645^2 * 0.5 * 0.5) / 0.04^2 = 423.3. Therefore, a sample size of 424 is required to achieve the desired margin of error and confidence level.

For the second question regarding the confidence interval for the percentage of seniors planning to go to college this year, the total sample size is the sum of students from all categories, which is 500. The proportion planning to go to college is 289/500. Using a formula for constructing a confidence interval for a proportion, C.I. = p ± (Z*sqrt(p(1-p)/n)), we can find our interval.

Testing the hypothesis regarding military enlistment involves setting up a null hypothesis (H0: p = 0.045) and an alternative hypothesis (H1: p ≠ 0.045), where p is the proportion of high school seniors enlisting in the military. The test statistic is calculated using a formula, and the P-value associated with this statistic is compared against the alpha level to decide whether to reject H0.

If considering undecided or no response students as potential enlistees changes this calculation significantly, we reassess by including an adjusted number of potential enlistees.

Answer:

$1,579.44; yes

Step-by-step explanation:

The student will have saved $2500 over the two month period and will be able to afford the computer.

In order to calculate the amount saved over a two month period, we need to calculate the monthly savings. To do this, we subtract the monthly expenses from the monthly gross salary:

$2,500 - $1,250 = $1,250

So the monthly savings is $1,250. To find the savings over a two month period, we multiply the monthly savings by 2:

$1,250 x 2 = $2,500

The cost of the computer is $1,500 plus 5.1% sales tax. To find the total cost, we multiply $1,500 by 1.051:

$1,500 x 1.051 = $1,576.50

Since the savings over a two month period is $2,500, and the total cost of the computer is $1,576.50, the student will be able to afford the computer and have savings left over.

Answer:

[tex]\sqrt{29}\ units[/tex]

Step-by-step explanation:

we know that

In a right triangle

Applying the Pythagorean Theorem

[tex]c^2=a^2+b^2[/tex]

where

c is the hypotenuse (the greater side)

a and b are the legs (perpendicular sides)

In this problem we have

[tex]a=2\ units\\b=5\ units[/tex]

substitute

[tex]c^2=2^2+5^2[/tex]

[tex]c^2=29[/tex]

[tex]c=\sqrt{29}\ units[/tex]

Answer:

Pamela = 30

Jiri = 40

Step-by-step explanation:

Two equations needed:

J-10 = P

P+J = 70

Plug and solve:

(J-10) + J = 70

2J - 10 =70

2J = 80

J = 40

40 - 10 = P

P=30

Answer:

30

Step-by-step explanation:

Let Jiri's age be x

Let Pamela's age be (x - 10)

The sum of their ages becomes

x + (x - 10) = 70

x + x - 10 = 70

2x - 10 = 70

2x =70+10

2x = 80

x = 40

Therefore, it means that Jiri's age is 40

Pamela's age is 40-10= 30

Answer:

Option C) 115 / square of 100 = 11.5

Step-by-step explanation:

We are given the following in the question:

Mean, μ = 496

Standard Deviation, σ = 115

Sample size, n = 100

a) Mean of scores

[tex]\bar{x} = \mu = 496[/tex]

b) The standard Deviation

[tex]s = \dfrac{\sigma}{\sqrt{n}} = \dfrac{115}{\sqrt{100}} = \dfarc{115}{10} = 11.5[/tex]

Thus, the correct answer is

Option C) 115 / square of 100 = 11.5

Answer:

Option C.  115 / square of 100 = 11.5.

Step-by-step explanation:

We are given that Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 496 and standard deviation 115.

An SRS of 100 students is chosen and average their SAT reading scores.

The z score normal probability is given by;

  Z = [tex]\frac{xbar-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)

So, the mean of the average scores will be close to [tex]\frac{\sigma}{\sqrt{n} }[/tex] i.e.;

      = 115 / square root of 100 = [tex]\frac{115}{\sqrt{100} }[/tex] = 115/10 = 11.5

The time for the fastest 10 % is less than 89.4 seconds

Here's how to find the qualifying task times:

Calculate the z-score for the 10th percentile:

A z-score represents the number of standard deviations a specific point is away from the mean. In this case, we want the z-score for the lower 10th percentile, which can be found using a z-score table or online calculators. The approximate z-score for the 10th percentile is -1.28.

Translate the z-score to task time:

We know the z-score for the 10th percentile (-1.28) and the standard deviation (20 seconds). We can use the formula to find the corresponding task time (t):

t = mean + (z-score) * standard deviation

t = 115 seconds + (-1.28) * 20 seconds

t ≈ 89.4 seconds

Therefore, task times less than 89.4 seconds qualify individuals for advanced training, as they fall within the lower 10th percentile of the normal distribution.

Complete question:

The time that it takes a randomly selected job applicant to perform a certain task has a distribution that can be approximated by a normal distribution with a mean value of 115 sec and a standard deviation of 20 sec. The fastest 10% are to be given advanced training. What task times qualify individuals for such training? (Round the answer to one decimal place.)

Answer:

A

Step-by-step explanation:

FOIL:First,Inner,Outer,Last

After the polynomial operations are done we can see that A is the answer.

6g*8g=48g^2

6g*3h=18gh

8g*-5h=-40gh

-5h*3h=-15h

After combining like terms we get :

48g^2-22gh-15h^2

THE ANSWER FOR CUP A IS 660 divided by 157

the answer to cup b is 660 divided by 628.319

brainliest plz

Answer:

0.008

Step-by-step explanation:

The probability of having chosen the unique dice three times in a row would be the multiplication of the probability of each event.

The event is always repeated. Take the single dice of 5 dice in total. Therefore the probability is 1/5.

Then the final probability would be:

(1/5) * (1/5) * (1/5), and that is equal to 0.008.

The probability that Cole picked the unique die given that he rolled three ones in a row is approximately 49.1%. This is calculated using Bayes' Theorem with the probabilities of rolling three ones with both the unique and regular dice.

Cole has 4 regular dice and 1 unique die that always rolls a 1. Let's calculate the probability that he picked the unique die given that he rolled three ones in a row.

First, find the probability of rolling three ones in a row using a regular die:

Second, since the unique die always rolls a 1, the probability of rolling three ones in a row with it is 1.

Using Bayes' Theorem, we calculate the probability that Cole picked the unique die:

Let A be the event that Cole picked the unique die.

Let B be the event that Cole rolled three ones in a row.

Thus, the probability that Cole picked the unique die is approximately 0.491 or 49.1%.

Answer:

a) The maximum revenue is ​$312500

b) The maximum​ profit is $89000, the production level that will realize the maximum​ profit is 1800, and the price the company should charge for each television set is $160.

C) If the government decides to tax the company ​$55 for each set it​ produces, the sets should the company manufacture each month to maximize its​ profit is 1250. the maximum​ profit is $70825 What should the company charge for each​ set is $187.5

Step-by-step explanation:

a) Revenue R(x)

R(x) = p(x) * x = x * [tex](250-\frac{x}{20})[/tex] = [tex](250x-\frac{x^{2} }{20})[/tex]

For maximum revenue, the first derivative of R(x) = R'(x) = 0

R'(x) = [tex](250-\frac{2x}{20}) = 0[/tex]

[tex](250-\frac{2x}{20}) = 0\\[/tex]

[tex]250=\frac{2x}{20}[/tex]

x = 2500

the second derivative of R(x)=R''(x)

R''(x) = -1/10 which is less than 0.

Maximum revenue is at x = 2500

R(2500) = [tex](250*2500-\frac{2500^{2} }{20})=312500[/tex]

b) Profit P(x)

P(x) = R(x) - C(x) = [tex](250x-\frac{x^{2} }{20})-(73000+70x) = -73000+180x-\frac{x^{2} }{20}[/tex]

For maximum profit, the first derivative of P(x) = P'(x) = 0

P'(x) = [tex]180-\frac{2x }{20}=0[/tex]

[tex]180=\frac{2x }{20}[/tex]

x = 1800

the second derivative of P(x)=P''(x)

P''(x) = -1/10 which is less than 0.

For maximum profit, x = 1800

Therefore P(1800)[tex]=-73000+180*1800-\frac{1800^{2} }{20}[/tex] = 89000

The price the company should charge for each television set is  p(1800) =[tex](250-\frac{1800}{20}) = 160[/tex]

c) f the government decides to tax the company ​$55 for each set it​ produces, the new cost C(x) = 73000 + 125x

Profit P(x)

P(x) = R(x) - C(x) = [tex](250x-\frac{x^{2} }{20})-(73000+125x) = -73000+125x-\frac{x^{2} }{20}[/tex]

For maximum profit, the first derivative of P(x) = P'(x) = 0

P'(x) = [tex]125-\frac{2x }{20}=0[/tex]

[tex]125=\frac{2x }{20}[/tex]

x = 1250

the second derivative of P(x)=P''(x)

P''(x) = -1/10 which is less than 0.

For maximum profit, x = 1250 hence 1250 sets should the company manufacture each month to maximize its profit

Therefore P(1800) =[tex]-73000+125*1250-\frac{1250^{2} }{20}[/tex] = 70825

The price the company should charge for each television set is  p(1250) =[tex](250-\frac{1250}{20}) = 187.5[/tex]

Answer:

5%

Step-by-step explanation:

According to fisher equation

Nominal rate = Real rate + Inflation

N = R + I

N is calculated when there is no inflation and for the current year = 8%

The Real rate is calculated from the base year

Real rate is consider "Inflation factor" and R is unknown

Inflation rate (I) = 3%

Hence, N = R + I

8 = R + 3

R = 8 - 3

R = 5%

Answer:

3^2

Step-by-step explanation:

3^5/3^3=3^(5-3)=3^2

Answer:

[tex] \frac{ {3}^{5} }{ {3}^{3} } = {3}^{5 - 3} = {3}^{2} = 9[/tex]

Step by step explanation :

When dividing two fraction we subtract the powers if the bases are same.

Answer:

756 is a reasonable estimate because the proportion of the sample whose favorite pizza is pepperoni is about 27 %

Step-by-step explanation:

given data

random sample = 150 people

favorite pepperoni pizza = 40

total of residents = 2800

number of residents favorite pizza = 750

solution

we get here first Proportion favorite pizza that is

Proportion = [tex]\frac{40}{150}[/tex]

Proportion = 0.27 = 27%

and now we get 27% of total of residents that is = 27% × 2800  

= 756

so we can say  756 is a reasonable estimate because here proportion of an sample whose favorite pizza are pepperoni pizza about 27 %